Bryan Oviedo and Darron Gibson have joined Sunderland on permanent deals for undisclosed fees.
Oviedo, 26, departs Everton having made 68 appearances for the Club over a four-and-a-half-year spell.
The Costa Rican joined the Blues from FC Copenhagen in August 2012 and will be fondly remembered by supporters for his match-winning goal at Old Trafford in December 2013.
Republic of Ireland midfielder Gibson played 69 times for the Toffees, scoring twice, including a memorable strike against Manchester City at Goodison Park just two weeks after his arrival from Manchester United in January 2012.
Blues boss Ronald Koeman says joining the Black Cats can give Oviedo and Gibson the chance for first-team football.
“It’s a good opportunity for them to play,” Koeman explained. “I’m happy for the boys. For Darron there was a lot of competition in midfield.
“In the situation of Bryan Oviedo, it was difficult. He was the back-up for Leighton (Baines) in the left-back position but finally I changed my mind, I spoke to the player and he was always the perfect professional. I understand his feelings. It was difficult for him. He’s got a new challenge to play in Sunderland. First of all (on him leaving) I said to him, ‘No way, no chance,’ because we need back-up and we need competition. But, as a football man, I changed my mind. I like the boy, he was working hard and that was the reason that he got the chance to go and play.
“It was difficult but I think if we get any problems in that position we have some good young ones and I think we can cope with the players we have in our squad.”